{"id":"W1972167756","doi":"10.48550/arxiv.1102.2460","title":"Spectra of Symmetrized Shuffling Operators","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Conjugacy class; Combinatorics; Reflection group; Symmetric group; Conjecture; Operator (biology); Simplex; Spectrum (functional analysis); Discrete mathematics; Pure mathematics; Coxeter group; Coxeter element","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003891085,0.0004526309,0.0009525922,0.0003815119,0.0000790048,0.00002116057,0.001081878,0.000451855,0.0001564485],"category_scores_gemma":[0.0006684552,0.0005090923,0.000376778,0.0005985285,0.0001571157,0.0001420673,0.001065221,0.0007426282,0.0000443684],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002408617,"about_ca_system_score_gemma":0.0001831671,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004797418,"about_ca_topic_score_gemma":0.000009323389,"domain_scores_codex":[0.9980984,0.0001287385,0.0005292344,0.0007270752,0.0001417636,0.0003747403],"domain_scores_gemma":[0.9968407,0.0005185761,0.0007533642,0.001428551,0.0002989257,0.00015994],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006412105,0.0002914866,0.0002211459,0.0006582384,0.0002203783,0.00008731974,0.0004497433,0.001412245,0.0001823079,0.9962982,0.00008471866,0.00003007692],"study_design_scores_gemma":[0.0008249923,0.00006652767,0.00001405116,0.00034808,0.0003416829,0.000002672009,0.0002295601,0.004025654,0.006223602,0.9873968,0.00004144184,0.0004848747],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8067631,0.000068387,0.1728365,0.000007508632,0.001251606,0.0007472151,0.00002832188,0.0003006886,0.01799667],"genre_scores_gemma":[0.9799255,0.0001149541,0.01882693,0.000007192004,0.00009893665,0.000001360075,0.000005280592,0.00008166546,0.0009382362],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1731623,"threshold_uncertainty_score":0.9997361,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.166961997758775,"score_gpt":0.2329905850447019,"score_spread":0.06602858728592689,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}